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A324559
Decimal expansion of the probability that the length of a chord drawn through 2 points taken at random within a circle on each side of a given diameter will be less than the radius.
1
3, 4, 1, 8, 0, 0, 5, 0, 8, 4, 0, 5, 4, 4, 4, 7, 0, 1, 2, 9, 7, 8, 0, 5, 2, 1, 4, 0, 3, 5, 4, 1, 1, 5, 1, 7, 0, 9, 4, 5, 0, 2, 3, 0, 9, 4, 1, 7, 6, 2, 9, 4, 1, 8, 2, 7, 1, 9, 6, 9, 2, 7, 6, 8, 4, 2, 6, 0, 0, 5, 2, 0, 4, 1, 2, 3, 5, 9, 6, 0, 0, 8, 2, 6, 1, 1, 1
OFFSET
-2,1
LINKS
J. J. Sylvester, Problem 1849, solved by Stephen Watson, Mathematical Questions with Their Solutions: From the "Educational Times", Vol. 8 (1868), pp. 92-93.
FORMULA
Equals 13/144 - 13*sqrt(3)/(48*Pi) + 3*(3 + log(4/3))/(16*Pi^2).
EXAMPLE
0.0034180050840544470129780521403541151709450230941762...
MATHEMATICA
RealDigits[13/144-13*Sqrt[3]/(48*Pi)+3*(3+Log[4/3])/(16*Pi^2), 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 06 2019
STATUS
approved